Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$x^{2}+328x+25=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
$$x=\frac{-328±\sqrt{328^{2}-4\times 25}}{2}$$
Square $328$.
$$x=\frac{-328±\sqrt{107584-4\times 25}}{2}$$
Multiply $-4$ times $25$.
$$x=\frac{-328±\sqrt{107584-100}}{2}$$
Add $107584$ to $-100$.
$$x=\frac{-328±\sqrt{107484}}{2}$$
Take the square root of $107484$.
$$x=\frac{-328±26\sqrt{159}}{2}$$
Now solve the equation $x=\frac{-328±26\sqrt{159}}{2}$ when $±$ is plus. Add $-328$ to $26\sqrt{159}$.
$$x=\frac{26\sqrt{159}-328}{2}$$
Divide $-328+26\sqrt{159}$ by $2$.
$$x=13\sqrt{159}-164$$
Now solve the equation $x=\frac{-328±26\sqrt{159}}{2}$ when $±$ is minus. Subtract $26\sqrt{159}$ from $-328$.
$$x=\frac{-26\sqrt{159}-328}{2}$$
Divide $-328-26\sqrt{159}$ by $2$.
$$x=-13\sqrt{159}-164$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-164+13\sqrt{159}$ for $x_{1}$ and $-164-13\sqrt{159}$ for $x_{2}$.
